Question: What is algorithm for this description?

assume i have a number 26 and assume a prime number not greater than a value, let it be 5

then it is like a division and factor into 5^2 + 1

if prime number set to 17, then it will output 17 + 3^2, 

the output will be in terms of prime number, such as  a^3+b^2 + c  where a and b are prime number

it should start from greatest prime number given as a parameter in function

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